Question

Suppose that a certain college class contains 65 students. Of these, 36 are freshmen, 34 are economics majors, and 9 are neither. A student is selected at random from the class.(a) What is the probability that the student is both a freshman and an economics major?(b) Given that the student selected is a economics major, what is the probability that she is also an freshman?Write your responses as fractions.

Answer 1

The answer is A

Explanation:

Answer 2

Answer: a) 14/65 b) 34/65

Step-by-step

Using set concept (venn diagram)

Let U be the total number if students

F be freshmen

E be economics majors

n(U) is the number of college class students i.e 65

n(F) to be number of freshmen i.e 36

n(E) to be economics major = 34

n(FuE)' be neither i.e 9

Students being both freshman and economics major is n(FnE) which is unknown

Prob ability that the student I both freshman and an economics major is n(FuE)/n(U)

To calculate n(FnJ), we use the formula

n(U) = n(F) + n(E) - n(FnE) + n(FuE)'

65 = 36 + 34 - n(FnE) + 9

65 = 79 - n(FnE)

n(FnE) = 14.

Probability = 14/65

b) If the student select economics major, probability that she is also a fresh men = n(E)/n(U) = 34/65 economics

That means that student studied economics and also among the freshmen :